An HN1 is a notice issued by the police under the Protection from Harassment Act 1997.
This means that as a result of your actions someone considers that you have harassed them in some way. There are several instances when harassment cannot occur, but I am not going to discuss that here.
However there are occasions when a complaint of harassment is false, if you are certain that that is the case and the complainant is lying that becomes misrepresentation, a 'false statement of fact' and could be considered one that is contractually binding, if you sign the HN1. No one is obliged to sign an HN1 no matter what the circumstances are.
Don't sign it